# Questions tagged [parabolic-pde]

A partial differential equation that describes diffusion phenomena.

22 questions with no upvoted or accepted answers
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### Form of nonlinear diffusion equation

Consider the following nonlinear diffusion problem, $$\frac{\partial u}{\partial t} = x^{-2}\frac{\partial}{\partial x}\left(x^2 u^4 \frac{\partial u}{\partial x}\right), \quad 0 < x < 1$$ We ...
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### Numerical scheme for the heat equation on the icosahedral hexagonal grid

I have a predefined grid(like this) that is spawned from a regular icosahedradron. It consists of many hexagons and 12 pentagons (corresponding to icosahedradron vertexes). I can tweak the granularity ...
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### Convergent Finite Difference Scheme for Parabolic Equation

Consider the PDE $$u_t = b_{11}u_{xx} + 2b_{12}u_{xy} + b_{22}u_{yy},$$ where $b_{11}, b_{22} > 0$, and $b_{12}^2 < b_1b_2$. In Strikwerda's book, the ADI scehme \begin{align*} \left( 1 - \frac{...
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1 vote
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### Oscillations when solving parabolic heat equation with FTCS

I'm wondering if someone could help me out, or point me in a direction of how I can understand the following oscillations that occur when I solve the Porous Medium Equation $$u_t = u_{xx}^{m+1}$$ ...
1 vote
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### Discretizing a parabolic PDE with finite volume method

I want to discretize the following parabolic PDE: $$u_t = \nabla\cdot(\alpha(x)\nabla u)- \beta u\\ x\in\Omega \subset \mathbb{R}^2\\ \partial_n u = 0\\ u(t,0) = u_0(x)\ge 0, \alpha(x)>0$$ Given ...
1 vote
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### Accuracy of finite difference method for heat equation on a disk

To study an approximation for the heat equation $$\frac{\partial^2 u}{\partial r^2}+\frac{1}{r}\frac{\partial u}{\partial r}+\frac{1}{r^2}\frac{\partial^2 u}{\partial\theta^2}=f(r,\theta)$$ on the ...
1 vote
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1 vote
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### explicit scheme stability restriction

Looking at the plain heat equation $u_t=u_{xx}$ the explicit scheme for it would look like the following iteration: $$u_{m,n+1}=\rho u_{m-1,n}+(1-2\rho)u_{m,n}+\rho u_{m+1,n}$$ I noticed this equation ...
1 vote